- NAME
- SYNOPSIS
- DESCRIPTION
- RETURN VALUES
- SEE ALSO
- HISTORY

# NAME

BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add, BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd - arithmetic operations on BIGNUMs

# SYNOPSIS

     #include <openssl/bn.h>

     int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);

     int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);

     int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);

     int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);

     int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
             BN_CTX *ctx);

     int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);

     int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);

     int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
             BN_CTX *ctx);

     int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
             BN_CTX *ctx);

     int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
             BN_CTX *ctx);

     int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);

     int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);

     int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
             const BIGNUM *m, BN_CTX *ctx);

     int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);

# DESCRIPTION

`BN_add()` adds a and b and places the result in r (`r=a+b`). r may be the same BIGNUM as a or b.

`BN_sub()` subtracts b from a and places the result in r (`r=a-b`).

`BN_mul()` multiplies a and b and places the result in r (`r=a*b`). r may be the same BIGNUM as a or b. For multiplication by powers of 2, use BN_lshift.

`BN_sqr()` takes the square of a and places the result in r (`r=a^2`). r and a may be the same BIGNUM. This function is faster than BN_mul(r,a,a).

`BN_div()` divides a by d and places the result in dv and the remainder in rem (`dv=a/d, rem=a%d`). Either of dv and rem may be NULL, in which case the respective value is not returned. The result is rounded towards zero; thus if a is negative, the remainder will be zero or negative. For division by powers of 2, use BN_rshift(3).

`BN_mod()` corresponds to `BN_div()` with dv set to NULL.

`BN_nnmod()` reduces a modulo m and places the non-negative remainder in r.

`BN_mod_add()` adds a to b modulo m and places the non-negative result in r.

`BN_mod_sub()` subtracts b from a modulo m and places the non-negative result in r.

`BN_mod_mul()` multiplies a by b and finds the non-negative remainder respective to modulus m (`r=(a*b) mod m`). r may be the same BIGNUM as a or b. For more efficient algorithms for repeated computations using the same modulus, see BN_mod_mul_montgomery and BN_mod_mul_reciprocal.

`BN_mod_sqr()` takes the square of a modulo m and places the result in r.

`BN_exp()` raises a to the p-th power and places the result in r (`r=a^p`). This function is faster than repeated applications of BN_mul().

`BN_mod_exp()` computes a to the p-th power modulo m (`r=a^p % m`). This function uses less time and space than BN_exp(). Do not call this function when m is even and any of the parameters have the BN_FLG_CONSTTIME flag set.

`BN_gcd()` computes the greatest common divisor of a and b and places the result in r. r may be the same BIGNUM as a or b.

For all functions, ctx is a previously allocated BN_CTX used for temporary variables; see BN_CTX_new.

Unless noted otherwise, the result BIGNUM must be different from the arguments.

# RETURN VALUES

For all functions, 1 is returned for success, 0 on error. The return value should always be checked (e.g., `if (!BN_add(r,a,b)) goto err;`). The error codes can be obtained by ERR_get_error.

# SEE ALSO

bn, ERR_get_error, BN_CTX_new, BN_add_word, BN_set_bit

# HISTORY

BN_add(), BN_sub(), BN_sqr(), BN_div(), BN_mod(), BN_mod_mul(), `BN_mod_exp()` and `BN_gcd()` are available in all versions of SSLeay and OpenSSL. The ctx argument to `BN_mul()` was added in SSLeay 0.9.1b. `BN_exp()` appeared in SSLeay 0.9.0. BN_nnmod(), BN_mod_add(), BN_mod_sub(), and `BN_mod_sqr()` were added in OpenSSL 0.9.7.